most stims like caffeine can cause acne in some people.. if your worried about increased acne id stop the coffee but the amounts your taking are very minimal and i would not stop srinking it..
i consume about 5 cups of coffees worth of caffeine a day(600mg) as part of my ec stack and have small acne on chest/back..
its not something to really worry about

I have never heard of caffeine being hard on your liver. I finished accutane in December and I took creatine, caffeine, and drank on the weekends in moderation and had no problems or elevated levels of whatever they measure in your liver. Just take milk thistle and drink lots of water and you will be fine.

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